0488733 - ÚJF 2019 RIV NL eng J - Článek v odborném periodiku
Behrndt, J. - Exner, Pavel - Holzmann, M. - Lotoreichik, Vladimir
On the spectral properties of Dirac operators with electrostatic delta-shell interactions.
Journal de Mathematiques Pures et Appliquees. Roč. 111, č. 3 (2018), s. 47-78. ISSN 0021-7824. E-ISSN 1776-3371
Grant CEP: GA ČR(CZ) GA14-06818S
Institucionální podpora: RVO:61389005
Klíčová slova: Dirac operator * self-adjoint extension * shell interaction * spectral properties
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 1.961, rok: 2018 ; AIS: 2.338, rok: 2018
DOI: https://doi.org/10.1016/j.matpur.2017.07.018

In this paper the spectral properties of Dirac operators A(eta), with electrostatic delta-shell interactions of constant strength eta supported on compact smooth surfaces in R-3 are studied. Making use of boundary triple techniques a Krein type resolvent formula and a Birman Schwinger principle are obtained. With the help of these tools some spectral, scattering, and asymptotic properties of An are investigated. In particular, it turns out that the discrete spectrum of A(eta), inside the gap of the essential spectrum is finite, the difference of the third powers of the resolvents of A(eta), and the free Dirac operator A(0) is trace class, and in the nonrelativistic limit A(eta), converges in the norm resolvent sense to a Schrodinger operator with an electric delta-potential of strength eta.
Trvalý link: http://hdl.handle.net/11104/0283275